Outline of Research
I am now interested in analyzing the global behavior of solutions to the nonlinear partial differential equations, especially parabolic equations and PDEs described by a biological phenomenon called chemotaxis, and the functional inequalities involved in that. Chemotaxis is phenomenon that cause migrations of cells or organisms in reaction to the concentration gradient of some chemical substances, and it is observed in various biological contexts.
Publications
Global existence and boundedness of solutions to a fully parabolic chemotaxis system with indirect signal production in $\mathbb{R}^4$
Tatsuya Hosono and Philippe Laurençot
Journal of Differential Equations 416 (2025), 2085-2133.
publisher link: https://doi.org/10.1016/j.jde.2024.10.035
arXiv link: https://doi.org/10.48550/arXiv.2404.01724
Global existence of solutions to the 4D attraction-repulsion chemotaxis system and applications of Brezis--Merle inequality
Tatsuya Hosono and Takayoshi Ogawa
Nonlinearity 36 (2023), 5860-5883.
publisher link: https://doi.org/10.1088/1361-6544/acf6ee
Finite-time blow-up for the attractive dominant case of an attraction-repulsion chemotaxis system in the whole space
Tatsuya Hosono
Differential and Integral Equations 36 (2023), 907-928.
publisher link: https://doi.org/10.57262/die036-1112-907
Local well-posedness and finite time blow-up of solutions to an attraction-repulsion chemotaxis system in higher dimensions
Tatsuya Hosono and Takayoshi Ogawa
Journal of Mathematical Analysis and Applications 510 (2022), 126009.
publisher link: https://doi.org/10.1016/j.jmaa.2022.126009
Proceedings (Peer-reviewed)
On the Cauchy problem of a chemotaxis system with indirect signal production
Tatsuya Hosono
accepted in SEMA-SIMAI SPRINGER SERIES volume entitled “Analysis, approximation and control of chemotaxis models.”
(These proceedings are based on the mini-symposia held at the 9th European Congress of Mathematics, organized by the European Mathematical Society, which took place in Seville, Spain, from July 15 to 19, 2024.)
Preprints
Nonlinear Fisher information, corresponding functional inequalities and applications
Tomasz Cieślak, Kentaro Fujie and Tatsuya Hosono
arXiv link: https://doi.org/10.48550/arXiv.2509.01475
Global solvability and threshold for a parabolic-elliptic chemotaxis system in $\mathbb R^n$
Tatsuya Hosono
OCAMI Preprint Series 2025 link: https://www.omu.ac.jp/orp/ocami/publications/preprint-series/2025/
Collaborators
Takayoshi Ogawa; Philippe Laurençot; Tomasz Cieślak; Kentaro Fujie
International conference
PDE seminar, Laboratoire de Mathématiques (LAMA), Université Savoie Mont Blanc, France, October 10, 2025, Invited:
Nonlinear Fisher information and its application to critical quasilinear fully parabolic Keller-Segel system
PDE seminar, L'Institut Elie Cartan de Lorraine, Nancy, France, September 11, 2025, Invited:
Global solvability and threshold for a parabolic-elliptic system of chemotaxis
9th European Congress of Mathematics, minisymposium, Sevilla, Spain, July 18, 2024, Invited:
Global existence and boundedness of solutions to the 4D chemotaxis system with indirect signal production.
PDE seminar at the Warsaw University of Technology, Warsaw University of Technology, Poland, June 6, 2024, Invited:
Global existence and boundedness of solutions to the 4D chemotaxis system with indirect signal production.
Online Seminar on Chemotaxis, Zoom, Apr 19, 2024, Invited: Global existence and boundedness of solutions to the 4D chemotaxis system with indirect signal production.
The 7th International Workshop on Mathematical Analysis of Chemotaxis, Kyoto, Mar 4, 2024, Invited: Global existence and boundedness of solutions to the 4D chemotaxis system with indirect signal production.
The 25th Northeastern Symposium on Mathematical Analysis, Hokkaido University, Feb 19, 2024, Poster: Global existence and boundedness of solutions to the 4D chemotaxis system with indirect signal production.
Critical phenomena in Nonlinear Partial Differential Equations, Harmonic analysis, and Functional inequalities -in honor of Professor Takayoshi Ogawa's 60th birthday-, Exhibition hall I-A,B, Exhibition Building, Sendai International Center, Nov 9, 2023, Invited: Global existence of solutions to the 4D fully parabolic chemotaxis system with indirect signal production.
The 24th Northeastern Symposium on Mathematical Analysis, Tohoku University, Feb 20, 2023, Invited: Global existence and $(8\pi)^2$-threshold of solutions the 4D attraction-repulsion chemotaxis system.
First Franco-Japanese Workshop on Chemotaxis Models, Tohoku University, Oct 20, 2022, Invited: Global existence of solutions to the 4D attraction-repulsion chemotaxis system and applications of Brezis--Merle inequalities.
The 23rd Northeastern Symposium on Mathematical Analysis, Online, Feb 21, 2022, Poster: Finite time blow-up of solutions to an attraction-repulsion chemotaxis system in the attractive dominant case.
The 22nd Northeastern Symposium on Mathematical Analysis, Online, Feb 15, 2021, Poster: Blow up for solutions to higher dimensional attraction-repulsion chemotaxis system related to Alzheimer's disease.
Japanese conference
九州関数方程式セミナー, 九州大学 西新プラザ, 2025年7月4日, 招待講演:
``Global solvability and threshold behavior for the Cauchy problem of a parabolic-elliptic chemotaxis system"
大阪大学微分方程式セミナー, 大阪大学, 2025年6月13日, 招待講演:
``Global solvability and threshold for a parabolic-elliptic chemotaxis system"
南大阪応用数学セミナー, 大阪公立大学, 2025年4月19日, 招待講演:
Global solvability and threshold for a parabolic-elliptic chemotaxis system
研究会「微分方程式論の拡がり」, 関西学院大学大阪梅田キャンパス K.G. ハブスクエア大阪 14F，1407教室, 2025年3月12日, 招待講演:
``Global existence and critical mass for a chemotaxis system with indirect signal production"
Critical Exponent and Nonlinear Partial Differential Equations 2025, 東京理科大学, 2025年3月7日, 招待講演:
``Global solvability and critical mass for a chemotaxis system"
第3回 信州若里偏微分方程式セミナー, 信州大学, 2024年11月9日, 招待講演:
空間 4 次元に於ける間接的シグナル生成を伴う走化性方程式の解の時間大域可解性と臨界質量について
日本数学会2024年度年会, 大阪公立大学, 2024年3月23日, 一般講演: Global existence and boundedness of solutions to the 4D fully parabolic chemotaxis system with indirect signal production.
第17回 若手のための偏微分方程式と数学解析, 九州大学 西新プラザ 大会議室 A・B, 2024年2月14日, 招待講演: Global existence and boundedness of solutions to the 4D fully parabolic chemotaxis system with indirect signal production.
第72回南大阪応用数学セミナー, 大阪公立大学, 2023年10月28日, 招待講演: 誘引反発型走化性方程式の4次元における解の時間大域存在について.
東北大学応用数理解析セミナー, 東北大学, 2023年10月19日, 招待講演: Global existence and boundedness of solutions to the 4D fully parabolic chemotaxis system with indirect signal production.
第12回福島応用数学研究集会, 福島大学, 2023年3月20日, 招待講演: Global existence and $(8\pi)^2$-threshold of solutions to the 4D attraction-repulsion chemotaxis system.
日本数学会2023年度年会, 中央大学, 2023年3月16日, 一般講演: Global existence of solutions to the 4D attraction-repulsion chemotaxis system and applications of Brezis--Merle inequality.
黒木場正城教授 追悼研究集会 「非線型偏微分方程式と走化性」, 北九州国際会議場 国際会議室(11/29-30)及び第11会議室(12/1), 2022年12月1日, 招待講演: Global existence of solutions to the 4D attraction-repulsion chemotaxis system and applications of Brezis--Merle inequality.
第43回発展方程式若手セミナー, オンライン, 2022年9月6日, 一般講演: Global existence of solutions to the 4D attraction-repulsion chemotaxis system and applications of Brezis--Merle inequalities.
東北大学応用数理解析セミナー, 東北大学, 2022年7月14日, 招待講演: Brezis--Merle inequalities and its application to the 4D attraction-repulsion chemotaxis system.
日本数学会2022年度年会, オンライン, 2022年3月30日, 一般講演: Finite time blow-up of solutions to an attraction-replusion chemotaxis system in four dimensional case.
日本数学会2021年度秋季総合分科会 函数方程式論分科会, オンライン, 2021年9月15日, 一般講演: Finite time blow-up of solutions to an attraction-repulsion chemotaxis system in higher dimensions.
第42回発展方程式若手セミナー, オンライン, 2021年9月1日, 一般講演: Finite time blow-up of solutions to an attraction-repulsion chemotaxis system in higher dimensions.
非線形PDE若手ワークショップ, オンライン, 2021年3月6日, 招待講演: Finite time blow up for solutions to the Cauchy problem of an attraction-repulsion chemotaxis system in higher dimensions.
東北大学大学院理学・生命科学2研究科合同シンポジウム2021, オンライン, 2021年2月19日, ポスター発表: アルツハイマー病を記述する誘引-反発型走化性方程式系の解の挙動.
東北大学応用数理解析セミナー, 東北大学, 2021年1月14日, 招待講演: アルツハイマー病を記述する誘引-反発型走化性方程式系の解の挙動.
Bourses France Excellence Japon 2025
Period: 1 Sep 2025 -- 31 Jul 2026 (11months)
Stay:
Université Savoie Mont Blanc, Chambéry, 2025/9/1 -- 2026/3/2 (Mentor: Prof. Philippe Laurençot)
Université Toulouse III - Paul Sabatier, Toulouse, 2026/3/2 -- 2026/7/31 (Mentor: Prof. Ariane Trescases)
Link : https://jp.ambafrance.org/Bourses-France-Excellence
Grant-in-Aid for Early-Career Scientists, covered by JSPS
Period：April 2025 -- March 2029
Research project：非線形拡散を伴う走性モデルの解構造と周辺理論の開拓
Budged Amount：4,680,000 Yen(Direct cost：3,600,000 Yen, Indirect cost：1,080,000 Yen)
Link : https://kaken.nii.ac.jp/ja/grant/KAKENHI-PROJECT-25K17274/
Grant-in-Aid for JSPS Fellows(PD)
Period：April 2025 -- March 2028
Research project：走化性方程式の解構造と臨界現象の数理解析
Budget Amount ：3,510,000 Yen(Direct cost：2,700,000 Yen, Indirect cost：810,000 Yen)
Link : https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-25KJ0279
Grant-in-Aid for JSPS Research Fellow(DC2), April, 2023 -- March, 2025
Research project：走化性方程式系に於ける臨界構造と解の大域挙動の解明
Budget Amount：2,000,000 JPY (Direct cost：2,000,000 JPY)
Link： https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-23KJ0150
Jul 2025 南北大阪勉強会 (in Japanese, Osaka Metropolitan University)
Aug 2025 Polish-Japanese One-Day Workshop on Mathematical Analysis at OMU (in English, Osaka Metropolitan University)
Regular Seminars
Apr 2021-Mar 2024 OS Special Seminar at Tohoku University (organized by doctoral students at Tohoku University)
Apr 2024-Mar 2025 Applied Mathematical Analysis Seminar (Tohoku University)
Apr 2025-Present South Osaka Applied Mathematical Seminar (Osaka Metropolitan University)